Physics - Classical Mechanics - Surface Tension

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Introduction

Hey it's a me again @drifter1!

Today we continue with Physics, and more specifically the branch of "Classical Mechanics", in order to talk about Surface Tension.

So, without further ado, let's get straight into it!

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Surface Tension

In the previous post about Buoyancy, while relating the concept to density we found out that only objects with a density less than that of the fluid can float. But, there are still cases where denser objects float. For example, a needle which is much denser than water still floats on top of it. This is caused by a phenomenon known as surface tension.

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Cohesive Forces

Responsible for surface tension are the cohesive (intermolecular attractive) forces between the molecules in a liquid. All molecules within a liquid interact with other molecules in all directions. But, in the case of the surface of a liquid, only inward cohesive forces are present, which makes those cohere more strongly to molecules on the surface.

Adhesive Forces

The forces of attraction between a liquid and a solid are called adhesive forces. Adhesion is basically the attractive force between unlike molecules. The difference between those and the cohesive forces determine the behavior the liquid shows when in contact with a solid surface.

S.I. Unit

Surface tension is calculated in N/m, but it's quite common to use cgs or dynes/cm, which equals 10^-3N/m = 1 mN/m.

The surface tension of water at 25°C is 72 dynes/cm. It decreases significantly as temperature increases.

Mathematical Definition

Surface tension is denoted by γ and is defined as:

where d is the total length of contact between the liquid.

Thus, if an object has length l, the total "distance" of contact would be d = 2l, as it would interact with the liquid on two sides or surfaces. Each side receives an equal force of:

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Capillarity

Surface tension also explains capillary action (or capillarity), which gives some liquids a concave and others a convex shape when confined in a tube. The meniscus is caused by the adhesive forces between the liquid and the glass material of the tube.

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Water rises at the side as the adhesive forces between it and the glass tube are stronger (water "wets" glass), whilst a fluid like mercury shows stronger cohesive forces, causing it to rise upwards in the middle.

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RESOURCES:

References

1. https://www.usgs.gov/special-topics/water-science-school/science/surface-tension-and-water
2. https://www.chem.purdue.edu/gchelp/liquids/tension.html
3. http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
4. https://en.wikipedia.org/wiki/Surface_tension

Images

1. https://pxhere.com/en/photo/1045542
2. https://commons.wikimedia.org/wiki/File:Surface_tension_March_2009-2.jpg
3. https://commons.wikimedia.org/wiki/File:Capillarity-small.svg

Mathematical equations used in this article, where made using quicklatex.

Visualizations were made using draw.io.

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Previous articles of the series

Rectlinear motion

• Velocity and acceleration in a rectlinear motion -> velocity, acceleration and averages of those
• Rectlinear motion with constant acceleration and free falling -> const acceleration motion and free fall
• Rectlinear motion with variable acceleration and velocity relativity -> integrations to calculate pos and velocity, relative velocity
• Rectlinear motion exercises -> examples and tasks in rectlinear motion

Plane motion

• Position, velocity and acceleration vectors in a plane motion -> position, velocity and acceleration in plane motion
• Projectile motion as a plane motion -> missile/bullet motion as a plane motion
• Smooth Circular motion -> smooth circular motion theory
• Plane motion exercises -> examples and tasks in plane motions

Newton's laws and Applications

• Force and Newton's first law -> force, 1st law
• Mass and Newton's second law -> mass, 2nd law
• Newton's 3rd law and mass vs weight -> mass vs weight, 3rd law, friction
• Applying Newton's Laws -> free-body diagram, point equilibrium and 2nd law applications
• Contact forces and friction -> contact force, friction
• Dynamics of Circular motion -> circular motion dynamics, applications
• Object equilibrium and 2nd law application examples -> examples of object equilibrium and 2nd law applications
• Contact force and friction examples -> exercises in force and friction
• Circular dynamic and vertical circle motion examples -> exercises in circular dynamics
• Advanced Newton law examples -> advanced (more difficult) exercises

Work and Energy

• Work and Kinetic Energy -> Definition of Work, Work by a constant and variable Force, Work and Kinetic Energy, Power, Exercises
• Conservative and Non-Conservative Forces -> Conservation of Energy, Conservative and Non-Conservative Forces and Fields, Calculations and Exercises
• Potential and Mechanical Energy -> Gravitational and Elastic Potential Energy, Conservation of Mechanical Energy, Problem Solving Strategy & Tips
• Force and Potential Energy -> Force as Energy Derivative (1-dim) and Gradient (3-dim)
• Potential Energy Diagrams -> Energy Diagram Interpretation, Steps and Example
• Internal Energy and Work -> Internal Energy, Internal Work

Momentum and Impulse

• Conservation of Momentum -> Momentum, Conservation of Momentum
• Elastic and Inelastic Collisions -> Collision, Elastic Collision, Inelastic Collision
• Collision Examples -> Various Elastic and Inelastic Collision Examples
• Impulse -> Impulse with Example
• Motion of the Center of Mass -> Center of Mass, Motion analysis with examples
• Explaining the Physics behind Rocket Propulsion -> Required Background, Rocket Propulsion Analysis

Angular Motion

• Angular motion basics -> Angular position, velocity and acceleration
• Rotation with constant angular acceleration -> Constant angular acceleration, Example
• Rotational Kinetic Energy & Moment of Inertia -> Rotational kinetic energy, Moment of Inertia
• Parallel Axis Theorem -> Parallel axis theorem with example
• Torque and Angular Acceleration -> Torque, Relation to Angular Acceleration, Example
• Rotation about a moving axis (Rolling motion) -> Fixed and moving axis rotation
• Work and Power in Angular Motion -> Work, Work-Energy Theorem, Power
• Angular Momentum -> Angular Momentum and its conservation
• Explaining the Physics behind Mechanical Gyroscopes -> What they are, History, How they work (Precession, Mathematical Analysis) Difference to Accelerometers
• Exercises around Angular motion -> Angular motion examples

Equilibrium and Elasticity

• Rigid Body Equilibrium -> Equilibrium Conditions of Rigid Bodies, Center of Gravity, Solving Equilibrium Problems
• Force Couple System -> Force Couple System, Example
• Tensile Stress and Strain -> Tensile Stress, Tensile Strain, Young's Modulus, Poisson's Ratio
• Volumetric Stress and Strain -> Volumetric Stress, Volumetric Strain, Bulk's Modulus of Elasticity, Compressibility
• Cross-Sectional Stress and Strain -> Shear Stress, Shear Strain, Shear Modulus
• Elasticity and Plasticity of Common Materials -> Elasticity, Plasticity, Stress-Strain Diagram, Fracture, Common Materials
• Rigid Body Equilibrium Exercises -> Center of Gravity Calculation, Equilibrium Problems
• Exercises on Elasticity and Plasticity -> Young Modulus, Bulk Modulus and Shear Modulus Examples

Gravity

• Newton's Law of Gravitation -> Newton's Law of Gravity, Gravitational Constant G
• Weight: The Force of Gravity -> Weight, Gravitational Acceleration, Gravity on Earth and Planets of the Solar System
• Gravitational Fields -> Gravitational Field Mathematics and Visualization
• Gravitational Potential Energy -> Gravitational Potential Energy, Potential and Escape Velocity
• Exercises around Newtonian Gravity (part 1) -> Examples on the Universal Law of Gravitation
• Exercises around Newtonian Gravity (part2) -> Examples on Gravitational Fields and Potential Energy
• Explaining the Physics behind Satellite Motion -> The Circular Motion of Satellites
• Kepler's Laws of Planetary Motion -> Kepler's Story, Elliptical Orbits, Kepler's Laws
• Spherical Mass Distributions -> Spherical Mass Distribution, Gravity Outside and Within a Spherical Shell, Simple Examples
• Earth's Rotation and its Effect on Gravity -> Gravity on Earth, Apparent Weight
• Black Holes and Schwarzschild Radius -> Black Holes (Creation, Types, How To "See" Them), Schwarzschild Radius

Periodic Motion

• Periodic Motion Fundamentals -> Fundamentals (Period, Frequency, Angular Frequency, Return Force, Acceleration, Velocity, Amplitude), Simple Harmonic Motion, Example
• Energy in Simple Harmonic Motion -> Forms of Energy in SHM (Potential, Kinetic, Total and Maximum Energy, Maximum Velocity), Simple Example
• Simple Harmonic Motion Equations -> SHM Equations (Displacement, Velocity, Acceleration, Phase Angle, Amplitude)
• Simple Harmonic Motion and Reference Circle -> SHM and Smooth Circular Motion, Reference Circle
• Simple Harmonic Motion Exercises -> 2 Complete Examples on Simple Harmonic Motion
• Simple Pendulum -> Simple Pendulum (Return Force, Small Angle Approximations, More Accurate Period, Gravity Approximation)
• Physical Pendulum -> Physical Pendulum (Return Torque, Small Angle Approximations, Estimating Moment of Inertia)
• Exercises around Pendulums -> Complete Examples on the 2 types of Pendulums (Simple, Physical)
• Damped Oscillation -> Damping Force, Total Force and Differential Equation, Motion Equations, Special Cases
• Forced Oscillation and Resonance -> Forced Oscillation (Differential Equation, Amplitude, Resonance)
• Exercises around Damped and Forced Oscillation -> Complete Examples on Damped Oscillation and Forced Oscillation
• Chaos and Chaotic Oscillation -> Chaos, Unpredictability and Randomness, Chaotic Oscillation

Fluid Mechanics

• Density and Pressure -> Fluids and Fluid Mechanics, Density, Specific Gravity, Pressure
• Measuring Pressure in Fluids -> Pressure in Fluids (Variation with Depth), Absolute and Gauge Pressure, Measuring Pressure
• Pascal's Principle and Hydraulics -> Static Equilibrium, Pascal's Principle, Hydraulic Systems
• Archimedes' Principle and Buoyancy -> Buoyant Force, Archimedes' Principle, Relation with Density

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Final words | Next up

And this is actually it for today's post!

Next time we will get into exercises throughout all the fluid static topics that we've covered...

See ya!

Keep on drifting!

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